Answer:
(x, y, z) = (36°, 60°, 84°)
Step-by-step explanation:
Using the given variable definitions we can write the equations expressing the problem conditions.
x + y + z = 180
y + z = 4x
z = y + 24
Substituting the second equation into the first, we have ...
x +4x = 180
x = 180/5 = 36
Substituting this value in the second equation and adding that to the third equation, we have ...
(y +z) +(z) = (4·36) +(y +24)
2z = 168 . . . . . . subtract y and collect terms
z = 84
y = 84 -24 = 60
The angle measures are ...
(x, y, z) = (36°, 60°, 84°)
